In this paper we address the state-feedback stabilisation of multi-input compartmental systems, by this meaning the design of a state-feedback matrix that preserves the compartmental property of the resulting feedback system, meanwhile achieving stability. We provide necessary and sufficient conditions for the stabilisability of compartmental systems whose state matrix is irreducible, and a sufficient condition for the problem solution when A is reducible. The results significantly improve upon existing Linear Programming conditions obtained for the general class of multi-input positive systems.
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